Substrate effect on hydrogen evolution reaction in two-dimensional Mo2C monolayers

The physical and chemical properties of atomically thin two-dimensional (2D) materials can be modified by the substrates. In this study, the substrate effect on the electrocatalytic hydrogen evolution reaction (HER) in 2D Mo2C monolayers was investigated using first principles calculations. The isolated Mo2C monolayer shows large variation in HER activity depending on hydrogen coverage: it has relatively low activity at low hydrogen coverage but high activity at high hydrogen coverage. Among Ag, Au, Cu, and graphene substrates, the HER activity is improved on the Ag and Cu substrates especially at low hydrogen coverage, while the effects of the Au and graphene substrates on the HER activity are insignificant. The improvement is caused by the charge redistribution in the Mo2C layer on the substrate, and therefore the HER activity becomes high for any hydrogen coverage on the Ag and Cu substrates. Our results suggest that, in two-dimensional electrocatalysis, the substrate has a degree of freedom to tune the catalytic activity.

www.nature.com/scientificreports/ functionalization and doping, more theoretical understandings of the HER processes and guides to improve the HER activity are still required to apply the 2D Mo 2 C to the electrocatalytic applications. 2D materials in electrocatalytic cells are placed on a metal substrate, which acts as an electrode. Because 2D systems are atomically thin unlike bulk materials, the substrate inevitably affects their surface chemistry. The effect may be considered insignificant because the catalytic reactions occur directly on the 2D materials, not on the substrate. However, this is not true: one famous counterintuitive example is the strong modification of chemical reactions in ultrathin oxide films on metal substrates, where the electron tunneling from the substrate plays a crucial role [38][39][40] . As such, it may be possible to optimize HER activity using substrates. Although there have been significant studies on chemically modifying MXenes and their HER electrocatalytic properties, the substrate effect on these materials is not yet understood. In this study, using density functional theory (DFT) calculations, we investigated the substrate effect on the HER activity of MXene. Here, we focus on Mo 2 C as a typical example of MXene and consider several metal substrates such as Ag, Au, Cu, and graphene. Based on the Sabatier principle, we estimated the catalytic HER activity using the calculated reaction free energy for hydrogen adsorption. Our results showed that the HER activity of the isolated Mo 2 C monolayer is higher than those of the isolated Ag and Au metal catalysts, but is comparable to that of the Cu catalyst. While the substrate effects of the Au and graphene were not significant, the HER activities of Mo 2 C on the Ag and Cu substrates were improved to be better than that of Cu. These improvements are caused by the modification of the effective charge of Mo atoms and consequent reduction of the Coulomb attraction between Mo 2 C and hydrogen. The results suggest that the substrate can be used for fine-tuning HER activity in two-dimensional electrocatalysis.

Results and discussion
It is well known that the catalytic activity of a material is strongly correlated with the reactant-material bond strength: a volcano-shaped graph is formed when the activity is plotted with the bond strength [41][42][43] . This is explained by the Sabatier principle, which states that catalytic activity is high when the bond strength is neither too strong nor too weak. If the bond strength is too weak, the surface cannot activate the catalytic reaction. If the bond strength is too strong, the product fails to dissociate; the optimal bond strength balances the two extremes. HER also involves complicate processes, and several factors such as reaction path and solvation could affect the HER activity. Based on the Sabatier principle, however, the HER activity can be simply quantified by the reaction free energy in hydrogen adsorption (ΔG) 28,44 , as defined in Method. Previous experiments have shown that an electrocatalyst with a ΔG close to the optimal value exhibits a high exchange current density, which is a measure of the electrocatalytic activity, and the exchange current density exponentially decreases as ΔG deviates from the optimal value 41,44,45 . ΔG has been a reasonable descriptor of the HER activity for a wide variety of metals and alloys and has been applied in the design of highly efficient catalysts 46,47 . Parsons suggested that the optimum value was approximately ΔG = 0 41 . Recent theoretical and experimental results have reported that the optimal ΔG (approximately − 0.4 eV) is slightly smaller than zero in alkaline electrolytes 45 .
Before we discuss the Mo 2 C monolayers, we consider the HER activity of metal substrates such as Ag, Au, Cu, Pt, and graphene. For the substrates, only the (001) surface was considered. Figure 2a shows the ΔG of the metal substrates with respect to the coverage of the hydrogen absorbed on the surfaces. The coverage is defined as the ratio of the number of absorbed H atoms to the total number of possible absorption sites. The Pt substrate had the smallest ΔG for each H coverage, and the ΔG for each H coverage increased in the order of Cu, Ag, Au, and graphene. The ranges of the ΔG were from − 0.37 to − 0.02 eV, from 0.14 to 0.30 eV, from 0.41 to 0.53 eV, from 0.50 to 0.97 eV, and from 0.89 to 1.53 eV, for Pt, Cu, Ag, Au, and graphene, respectively. These results are in good agreement with previous findings 44,45 . In the graphene substrate, ΔG abruptly decreases to − 0.79 and − 0.54 eV at the two high coverages of 0.75 and 1.0, respectively. This is related to the qualitative change in the C π-bonding network accompanied by the metal-to-insulator transition [48][49][50][51] . In this regard, we distinguish the two results (open violate circle) from the others in low coverages in Fig. 2, because an insulator cannot be an electrocatalyst. Although the ΔG of both Pt and Cu were close to zero, the experiments clearly show that Pt is the better HER catalyst compared to Cu 44,45 . The results indicate that the optimal ΔG is close to, but smaller than zero. Therefore, in the following, we set the optimal value to the average ΔG of Pt (− 0.18 eV), which is represented by the horizontal lines in Fig. 2a,b. This indicates as the ΔG approaches the optimal value, the catalysis of HER activity increases.
Next, we consider the HER activity, i.e., ΔG, of Mo 2 C. To date, many studies have considered the Mo 2 C 1T phase, despite it being less stable than the 2H phase 52,53 . Here, we focused on the 2H phase. As shown in Fig. 1a, Mo 2 C has three absorption sites for hydrogen atoms, such as the top of a hexagonal center (TH), a C atom (TC), and a Mo atom (TM) (see Fig. 1a). We placed a H atom on each site and optimized the atomic structures. The H atom is the most stable at the TH site. The TC site is metastable, and its energy is higher by 0.20 eV than that of the TH site. The TM site is unstable, and the H atom moves to the stable TH site during ionic relaxation. In high H coverages, the TH sites of H atoms also have lower energies than the other sites. In this regard, we calculated the ΔG of the TH sites, and the results are shown in Fig. 2a,b. For the isolated Mo 2 C monolayer, ΔG varies from − 0.71 eV for low hydrogen coverage (0.0625) to − 0.37 eV for full hydrogen coverage (1.0). To check the calculational accuracy in our systems, we have also compared the PBE functional results with the RPBE functional ones, and as shown in Fig. 2b, the two results are in good agreement within 0.03 eV. In this regard, we conclude that, in the systems that we considered, the PBE functional also provides reasonable results with the same accuracy level of the RPBE functional.
To directly compare the HER activity of Mo 2 C with those of the metal substrates, we plotted the volcanoshaped HER activity with the peak located at the optimal ΔG in Fig. 3. The ΔG of Cu, Ag, Au, and graphene were all positive and located on the right of the optimal value. The HER activity of the Cu substrate was expected to be higher than the other substrate except Pt. The results of the graphene substrate are not shown in Fig. 3 Fig. 3.
The HER activity of Mo 2 C was expected to be higher than that of Ag and Au, but comparable to that of Cu. The HER activity of Mo 2 C was broader than that of Cu, and the HER activity was lower with low H coverage, but it was higher for high H coverage. The HER activity can be affected by the metal substrate of Mo 2 C. Figure 1b shows the atomic structure of Mo 2 C on a substrate: the Mo 2 C was placed on the (001) surface of the substrate. There was no strong bonding between the Mo 2 C and substrates, but a heterostructure was formed by a weak dispersive interaction. The atomic structures indicated that the physical properties of Mo 2 C were not significantly altered by the substrates. Using these structures, we calculated the ΔG of Mo 2 C on Cu, Ag, Au, and graphene substrates, and the results are shown in Fig. 2a,b. The ΔG values for all cases are distributed in the range from − 0.74 to − 0.35 eV, which is similar to the range of the isolated Mo 2 C case (− 0.71 ~ − 0.37 eV). These results indicate that Mo 2 C is dominant in determining ΔG because the H atoms directly bond to Mo 2 C, and the substrate effects are secondary. However, there are some ΔG differences that are attributable to the substrate. On the Cu and Ag substrates, the variation of ΔG was significantly reduced: while the ΔG for high coverages is similar to that of the Mo 2 C monolayer, the ΔG for low coverage increases from that of the Mo 2 C monolayer. This ΔG change results in the high HER activity for all H coverages. As shown in Fig. 3, the overall HER activity becomes better than that observed in the isolated Cu substrates, as the ΔG approaches the optimal value. Thus, the HER activity of 2D Mo 2 C can be adjusted by the substrate. For Mo 2 C on Au and graphene substrates, on the other hand, the changes in ΔG with H coverage are similar to those of the isolated Mo 2 C monolayer, which implies that the effects of the two substrates are negligible. Previous work suggested that HER activity can be improved in small Mo 2 C clusters on clean/nitrogen-doped graphene substrates 54 . Note that our results have only considered the pure 2D Mo 2 C fully covered on clean graphene surfaces, and in different structures such as the small Mo 2 C clusters in the previous work the substrate effect could be significant. We also considered the two Mo 2 C layers on the Ag substrate. As shown in Fig. 2b, the ΔG (red open triangle) decreases from ΔG of the Mo 2 C monolayer on the Ag substrate and approaches toward ΔG of the isolated Mo 2 C. As one may expected, this is because the substrate effect is reduced, when more Mo 2 C layers are stacked on the substrate.
While we have focused on the Mo 2 C 2H phase until now, the substrate can also tune the HER activity of the Mo 2 C 1T phase. As shown in Fig. 2b, ΔG of 1T Mo 2 C varies from − 0.53 eV (at the coverage 0.125) to − 0.41 eV (at the full coverage 1.0). On the Ag substrate, i.e., 1T Mo 2 C on the Ag substrate, ΔG is changed to the range from − 0.46 eV (at the coverage 0.5) to − 0.35 eV (at the low coverage 0.0625). Similar to the 2H Mo 2 C, the HER activity of 1T Mo 2 C can be also improved on the Ag substrate.
The increase in ΔG for low H coverage on the Cu and Ag substrates indicates the weakening of the bond strength between Mo 2 C and H. To understand the change in the bond strength, we performed Bader charge analysis, as shown in Table 1. In the Mo 2 C without a substrate, some of the six valence electrons in the Mo atom are transferred to the C atoms, resulting in positively charged Mo ions and negatively charged C ions. Bader charge analysis shows quantitative changes in the valence electrons: each Mo atom in Mo 2 C has 5.434 valence electrons, which implies that the Mo atom loses 0.566 electrons and thus the effective charge of the Mo ion becomes + 0.566. When an H atom is absorbed in the TH site of Mo 2 C, it forms bonds with the three nearest neighboring Mo atoms. Figure 4 shows the charge redistribution in the formation of the bonds, which is calculated by subtracting charge densities of the isolated Mo 2 C ρ Mo 2 C (r) and H atom ρ H (r) from that of the H absorbed Mo 2 C ρ Mo 2 C+H (r) , i.e., ρ Mo 2 C+H (r) − [ρ Mo 2 C (r) + ρ H (r)] . As shown in Fig. 4, the charge density increases near the H atom, but it decreases near the three Mo atoms. This indicates that the electrons in the three Mo atoms are transferred to the H atom and as a result the H atom becomes negatively charged. Using Bader  Table 1, we quantify the effective charges of the three Mo and H atoms to be + 0.658 and − 0.453, respectively. Beside the bonding between the H and Mo atoms, Coulomb attraction between the positively charged Mo and negatively charged H atoms induced by charge imbalance increases the bond strength.
The substrates modify the charge imbalance and thus the Coulomb attraction. For the Mo 2 C on the Ag and Cu substrates, the valence electrons in the Mo atoms increased to 5.502 and 5.492, respectively, compared to the isolate Mo 2 C (5.434). This indicated that the Ag and Cu substrates donate electrons to the Mo 2 C layer, and as a result the effective charge of the Mo atoms is reduced to + 0.498 and + 0.508 on the Ag and Cu substrates, respectively. This reduction also affects the effective charge of the Mo atoms after H absorption, and as shown in Table 1, the effective charges of the nearest neighboring Mo atoms became + 0.605 and + 0.604 on the Ag and Cu substrates, respectively, which is smaller than that of the isolated Mo 2 C (+ 0.658). On the other hand, the effective charge of the absorbed H atom (~ − 0.45) remains nearly the same for the different substrates (see Table 1). This is because the hydrogen bonding level is located far below Fermi level. Figure 5a,b show the density of states of the H absorbed Mo 2 C and Mo 2 C on the Ag substrate. For the both cases, the hydrogen bonding level is located around − 4.7 eV by level interaction between the Mo d-orbitals and H s-orbital (see Fig. 5c), while the Mo d-bands are distributed near the Fermi level. As such, the effective charges of the Mo atoms are easily changed by the substrates, but the effective charge of the H atom is not. Thus, the reduction of the effective charge of the Mo atom weakens the Coulomb attraction between the Mo and H atoms in the Mo 2 C on the Ag and Cu substrates, thereby increasing ΔG. On the other hand, for the Mo 2 C on the Au substrates, the electric charges of the Mo atoms are similar to those in the isolated Mo 2 C; thus, the variations of ΔG shown in Fig. 2 are also similar to those of the isolated Mo 2 C. Thus, the charge redistribution caused by the substrates can affect the HER activity of the 2D Mo 2 C.
Here we have focused on the Mo 2 C as a typical example of MXene. There are other MXenes such as Ti, Nb, Cr-based MXene, and these are also atomically thin two-dimensional systems. As such, a substrate can alter the electronic properties of a whole MXene in contrast to conventional bulk materials, of which the properties are changed only in the interface region. For example, as shown in Table 1, substrates change the effective charge of all the Mo atoms in the Mo 2 C monolayer, which affects the HER activity. In this regard, we believe that the substrates can also alter the HER activity of the other two-dimensional MXenes, and this could provide a way to tune the catalytic activity of two-dimensional MXenes.

Summary
In summary, we investigated the substrate effect on the HER activity of 2D Mo 2 C and compared its activity with that of metal catalysts such as Ag, Cu, Au, and graphene. The HER activity of the isolated Mo 2 C exhibits relatively large variation depending on the hydrogen coverage, showing low activity at low hydrogen coverage and high activity at high hydrogen coverage. While the substrate effect is not significant, we have shown that Ag and Cu substrates can tune the HER activity of Mo 2 C, especially at low hydrogen coverage, such that HER activity becomes high for all H coverages. Our results suggest a method for tuning the HER activity of two-dimensional electrocatalysis.

Methods
The optimized geometries and relevant total energies were calculated using DFT calculations 55,56 with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional 57 , as implemented in the Vienna ab initio simulation package 58 . Previous work has shown that the revised PBE (RPBE) functional provides more accurate adsorption energy than the PBE functional. 59 We have also tested the accuracy of the PBE functional in our systems and found that the PBE functional results are in good agreement with the RPBE functional ones within 0.03 eV (see Fig. 2b). The projected augmented wave potentials were used to represent the ion cores 60,61 . The wave functions were expanded in a plane wave basis set up to a cut-off energy of 400 eV. To model the Mo 2 C monolayer (see Fig. 1a), we used a periodic supercell containing 48 atoms (4 × 2 √ 3 unit cells). For the Ag, Au, Cu, and Pt substrates, we employed periodic slab models containing six atomic layers along the (001) direction. In all the calculations, the slabs were separated by a vacuum gap of at least 20 Å. The 2 × 2 × 1 Monkhorst-Pack k-point mesh was used for Brillouin-zone integration. We used optimized lattice parameters for the Mo 2 C and substrates and the lattice parameters of the Mo 2 C monolayer for the Mo 2 C on a substrate (Fig. 1b). In all the cases, the lattice mismatches were below 10%, and the effect of the lattice mismatches was small because hydrogen atoms are directly bonded to Mo 2 C, not the substrates. Note that the metallicity of the Mo 2 C monolayer is maintained under tensile and compressive strain. We fixed the positions of the atoms in the two bottom layers of the substrates, and the atomic positions of the other atoms were fully relaxed until the residual forces were less than 0.01 eV/Å.
The HER activity was measured using the variation of the reaction free energy in hydrogen adsorption ΔG, represented by where ΔE H , ΔZPE, and ΔS are the changes in the DFT total energies, zero-point energy, and entropy of a hydrogen atom when absorbing an electrocatalyst from an H 2 molecule, respectively, and T is the system temperature. Here, we consider standard conditions (T = 298.15 K, p = 1 bar, pH = 0), i.e., acidic HER process, and (ΔZPE − TΔS) is set to 0.24 eV 28,44,54,62,63 . ΔE H can be calculated using either